Yes...when you say that you mean Marmoset and Tamarin monkeys. I breed Cotton Top Tamarins..They are only the size of your finger when they are babies though...fully grown they both weigh about a pound, so they are still small.
They are a lot of work though, as they are highly intelligent creatures.
Please see the related link below.
Actually there is a type of monkey that is the size of your finger when full grown; it is the Pygmy Marmoset. There is a picture of two of them at the second related link below.
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